Fire Heat Flux to Unwetted Vessels for Depressuring Calculations

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Fire Heat Flux to Unwetted Vessel for Depressuring Calculations

Saeid Rahimi

25-Nov-2012

Introduction

Depressuring calculation is one the subject that has been greatly developed over the past decade. The use of software has

extremely improved the accuracy and speed of the calculations too. However, providing the proper inputs to the software in one

hand and utilizing the available software capabilities to produce the meaningful results on the other hand has ended up with lots

of lessons learned. One of the lessons learned was that using Fire API521 heat input model (originally developed for the

wetted vessels) in Hysys for an unwetted vessel results in zero heat flux as the actual wetted area of this type of vessel is zero.

Then, engineers started exploring how to define this parameter in the depressuring calculations.

They noticed that API-521, 5th

edition, section 5.15.1.2.2 states that the recent calculation indicates that heat flux of the fire is

in the range of approximately 80 to 100kW/m2. This is based on the test results published in the Annex 1, Table A.1 of the

same standard for wetted vessels. The results of the same test have been used by API committee to introduce q = 70.7 F A0.82

(q

in kW, where there is no draining facility) for calculation of heat fluxes to the wetted vessels.

Therefore, in absence of any standard guideline for the depressuring, many used this range (typically 100kW/m2) as the heat

input for depressuring calculations of unwetted (gas filled) vessels. This note reviews the adequacy of this range for thedepressuring calculations and recommends the alternative method of defining the fire heat flux to the unwetted vessels.

Fire Heat Flux

As discussed in the note The Effect of Different Parameters on Depressuring Calculation Results, the following equation is

usually used in Hysys depressuring utility to define the heat input to the gas filled vessels1:

q = C1+ C2time + C3(C4 Vessel Temp) + C5LiqVol(time = t)/ LiqVol(time = 0) (1)

Where

C1= Q A

Q = 80-100 kW/m2

C2= C3= C4= C5= 0

Using equation (1) with above coefficients seems to resolve the problem of setting fire heat flux, however, it introduces new

questions. For example:

This value seems to be high at the first glance compared to the wetted vessel heat flux. According to the above equation (q= 100 A), the gas inside an unwetted vessel with the surface area of 1 m

2can absorb 100kW while the wetted vessels heat

absorption formula q = 43.2 F A0.82

(where there is a proper draining facility) predicts that liquid absorbs 43.2kW per each

square meter of wetted surface (assuming F=1.0). The higher heat transfer to the gas through the unwetted surface totally

contradicts the heat transfer fundamentals.

Considering the constant heat flux of 100kW/m2 will result in highly unreasonable final temperature (sometimes beyond2000C) in Hysys depressuring results. This is because the vessel gas content is depleted as depressuring continues while

heat input remains constant causing the gas temperature to increase drastically. Therefore, using the constant heat fluxmethod which does not take the vessel internal and external heat transfer coefficient into account may not be correct.

Heat Transfer Rate

From the heat transfer viewpoint, the fire heat is absorbed by the vessel metal through the radiation and convection in the first

step. Then, depending on the metal surface temperature, part of the absorbed heat is radiated back to the surroundings and the

rest of the heat is accumulated in the system (vessel metal + vessel fluid) by time causing temperature to increase. The amount

of the heat transferred from the fire to the vessel body is the function of many parameters which is out of the scope of this notebut looking at heat transfer background of this phenomenon will help to understand the difference between the wetted and

unwetted vessels exposed to fire:

1Compared to Hysys Fire API521, for fire depressuring calculations of wetted vessels:

q = C1C3(Wetted Area)^C2Where q is in kW, C1= 43.2, C2= 0.82 and C3= 1


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External Heat Transfer Mechanism

The external free/force convection is the same for both wetted and unwetted vessel as it is related to the fire condition notto vessel fluid. The external heat radiation to the wetted vessels should be a bit higher than the unwetted vessels as the wall

temperature is lower in the wetted vessel due to high internal heat transfer coefficient which keeps the wetted wall cool.

Despite the difference between the wall temperatures, since the flame temperature is the same for both cases and much

higher than wall temperatures, therefore the radiation heat transfer to the wetted and unwetted vessel will be almost

identical.

This means that what is transferred from the fire to the vessel metal will be almost constant irrespective of the vessel type.

Therefore, the API statement that 80-100 kW/m2 is transferred from the fire to the vessel should be correct.

Internal Heat Transfer Mechanism

For the wetted vessel, the internal heat transfer mechanism is boiling which provides extremely high heat transfer

coefficient. For the unwetted vessels, the internal heat transfer mechanism is mainly free convection with some radiations

at high metal temperatures. But in general the rate of heat transfer through free convection and radiation is lower than thewetted vessel.

This means that almost all the heat absorbed by metal during fire will be transferred to liquid whereas only part of it will

be absorbed by gas in unwetted vessels. The rest of the heat input which is not absorbed by the fluid is used to heat up the

metal, reducing its strength and leading to an earlier failure.

Therefore, the wall temperature of unwetted vessels will be much higher than the wetted ones as the heat absorption rate is

much higher than the heat dissipation rate. Furthermore, the overall heat input to the gas inside the unwetted vessel should be

lower than 100kW/m2 as the heat transfer resistance between the gas and metal is more than liquid and metal.Based on the above paragraph, the heat transfer resistance inside the unwetted vessel is much higher than the external

resistance, therefore, neglecting the radiation from the vessel wall to the gas, the overall heat transfer rate from the fire to the

gas is mainly controlled by the vessel internal free convection heat transfer which can be calculated through equation (2):

TAhq i (2)

In order to further simplify the solution of this equation, with the following assumptions are made:

1) The first minutes of the fire during which the vessel wall temperature sharply increases is ignored.

2) The maximum wall temperature is 593C (1100F) during depressuring. This is not very realistic assumption as the flame

temperature is much higher than 593C, driving the system towards the higher temperatures. However, considering the fact

that depressuring is started on the onset of fire, and just for the purpose of this calculation credit can be taken for the fire

water and depressuring systems to prevent very high metal temperatures. Furthermore, there is high likely that vessel wontwithstand the temperature higher than 593C for a long time; therefore there is no point in protecting a vessel which has

already failed.

For such conditions (isothermal surface), the free convection heat transfer

coefficient can be calculated using the following equations:

mPrGrCNu (3)

Where,

2

32 xTgGr

,

k

CPr

p ,k

xhNu , gw TTT

Therefore, the internal free convection heat transfer coefficient can becalculated by equation (4).

mp

m

2

32

k

CxTg

x

kCh

(4)

Replacing

avT

1 in equation (4) where

2

TTT

gwav

:

(5)

NOMENCLATURE

A Vessel surface area exposed to fire, m

C Constant

Cp Gas heat capacity, J/kg K

D Vessel diameter, m

L Vessel length, m

g Gravity acceleration, 9.81m/s

Gr Grashof number, dimensionless

h Heat transfer coefficient, J/s m2

Kk Gas thermal conductivity, J/s m K

m Constant

Nu Nusselt number, dimensionless

P Prandtl number, dimensionless

q Fire heat input, kW

qi Internal heat transfer rate, kW

Q Heat flux, kW/m2

Tg Vessel gas temperature, K

T Vessel wall temperature, K

Tav Gas average temperature, K

x Characteristic dimension, m

Cubical expansion coefficient, 1/K Gas dynamic Viscosity, kg/m s Gas density, kg/m3

m

av3m

1

1

m

1

p2

T

T

x

kCgCh


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Equation (5) clearly shows that systems with the

higher gas density (higher pressure, higher molecular

weight, lower temperature) have higher heat transfer

coefficient. My past experience in heat transfer

calculations also reveals that for most process vessels,

flow on the inner surface of the vessel will be

turbulent (109

< Gr Pr < 1013

) whereas the laminar

flow (104

< Gr Pr < 109) is observed in very low

pressure (basically atmospheric) systems.

Case Study

Table 2 shows the fire heat flux to a horizontal vessel with total surface area of 20m2, containing Methane at initial

temperature and pressure of 0C and 100bar. It assumes that the wall temperature is at 593C to calculate the internal free

convection heat transfer coefficient when the gas temperature increases from the initial to very close to the wall temperature.

Table 2- Internal Heat Transfer Calculation for Methane at Different Temperatures

Tg C 0 100 200 300 400 500

Tav C 297 347 397 447 497 547

at Tav kg/m3 33.555 30.675 28.279 26.250 24.507 22.990Cp at Tav J/kg C 3254.5 3421.2 3589.5 3754.6 3913.4 4063.4

at Tav kg/m s 1.97E-05 2.07E-05 2.18E-05 2.28E-05 2.39E-05 2.49E-05k at Tav J/m s C 8 .38E-02 9.29E-02 1.02E-01 1.12E-01 1.22E-01 1.32E-01

Gr - 3.70E+12 1.71E+13 9.71E+12 5.29E+12 2.60E+12 9.48E+11

Pr - 0.765 0.764 0.764 0.765 0.766 0.767

Gr Pr - 2.83E+12 1.30E+13 7.42E+12 4.05E+12 1.99E+12 7.27E+11

h W/m2

C 308.1 284.0 259.1 231.7 199.0 154.1

Q kW/m2

182.74 140.03 101.85 67.90 38.42 14.34

According to the results, the internal heat flux from the

wall at 593C to the Methane at 100 bar and lowtemperatures can be as high as double of API fire flux

range. For this particular system, this means that the

entire heat from the fire (100kW/m2) is initially

transferred to the gas inside the vessel before the heat

flux drops due to the reduction in heat transfer

coefficient and more importantly the differentialtemperature between the vessel wall and the gas. The

heat flux calculated in the above example is almost the

highest value possible among all other hydrocarbon

gases. Table 3 summarizes the effects of the pressure

on the free convection heat transfer coefficient from the vessel wall at 593C to the different gases for comparison.

Another case study for the same vessel at the conditions mentioned above indicates that if it is assumed that the walltemperature during the depressuring is always 200C above the gas temperature (when the gas temperate increases from 0C

to 500C - not constant), the heat flux from the vessel wall to Methane will be in the range of 40 to 50kW/m2

which is almost

the half of the heat flux from the fire to the vessel.

Conclusion

80-100 kW/m2

is the total heat input to the unwetted system (metal and content). However, depending on the gas heat transfer

features, all or part of this heat is transferred to the gas inside the vessel. Therefore, considering fire heat flux of 80 to

100kW/m2

for unwetted vessel depressuring calculation during the fire may result in unrealistic size for depressuring system

depending on the system conditions. This value is certainly conservative for relatively low pressure systems but it may be fairlyvalid for the high pressure systems. Therefore, it should be verified on case by case basis.

Based on the above observations, there are two methods to build a realistic Hysys model for the unwetted vessels with respectto the fire heat input:

Table 1 Equation 5 Coefficients

Vessel type Gr Pr C m x

Vertical 10

4-10

9

109-10

130.590.10

1/41/3

L

Horizontal10

4-10

9

109-10

130.53

0.13

1/4

1/3 D

Table 3- Internal Heat Transfer Coefficient for Different Gases

Composition Pressure

(bar)

Temp.

(C)

h

(kW/m2

C)

Heat flux

(kW/m2)

Methane 100 0 0.308 182.7

Methane 10 0 0.065 43.2

Methane 1 0 0.011 6.6

Ethane 10 0 0.080 76.8

Air 100 0 0.173 102.9

Air 1 0 0.006 3.6


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1. Using the Fire model (equation (1)) with the following settings along with the heat loss model of None to simulate the

net heat input to the gas which is important from the depressuring point of view.

C3= h A (kW/C)

C4= 593C

C1= C2= C5= 0

This is nothing but reproducing equation (2) by using available tools in

Hysys. This method produces sensible results as the gas temperature islimited to the reasonable plate temperature and the heat input to the gas is thefunction of time as the gas temperature (Vessel Temp in equation 1) is

changing by time.

By use of the maximum heat transfer coefficient from Table 3 (Methane at

100bar and 0C), C3for the above example can be set at:

C3= 0.308 kW/m2C x 20 = 6.0 kW/C.

Using this value is conservative because:

The heat transfer coefficient decreases as the system pressure reducesduring depressuring. Refer to Table 3 where heat transfer coefficient

decreases from 0.308 kW/m2C at 100bar to 0.065kW/m

2C at 10bar. Figure 1 Hysys Fire Heat Flux Equation

The heat transfer coefficient decreases as the gas temperature increases during fire depressuring. Refer to Table 2 whereheat transfer coefficient decreases from 0.308 kW/m

2C at the gas temperature of 0C to 0.154kW/m

2C at 500C.

2. Using the Fire model (equation (1)) with the following settings along with the Detailed heat loss model to include the

vessel metal mass and other ambient conditions which will help to have the realistic heat input to the gas. Figure 2 shows some

of the inputs to Hysys Detailed heat loss model.

C1= 100 A (kW)

C2= C3= C4= C5= 0

This approach will produce the realistic results for depressuring rate but the problem of the unrealistic final temperature will

remain unresolved.

Figure 2 Hysys Depressuring Detailed Heat Loss Model Parameters

Contact

Please feel free to contact [email protected] [email protected] should you have any comment, question or

feedback.

Fire Heat Flux to Unwetted Vessels for Depressuring Calculations

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